The area of a circle having the lines 3x - 4y | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given equations of the parallel tangents are $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$.To make the coefficients of $x$ and $y$ identical,multipl

Vedclass · Accepted Answer

$\frac{9\pi}{16}$

Vedclass · Answer

(B) The given equations of the parallel tangents are $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$.To make the coefficients of $x$ and $y$ identical,multiply the first equation by $2$:$6x - 8y + 8 = 0$ and $6x - 8y - 7 = 0$.The distance between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ is given by $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$.Here,the distance between the tangents is the diameter of the circle:$d = \frac{|8 - (-7)|}{\sqrt{6^2 + (-8)^2}} = \frac{15}{\sqrt{36 + 64}} = \frac{15}{10} = \frac{3}{2}$.Since the diameter is $\frac{3}{2}$,the radius $r = \frac{d}{2} = \frac{3}{4}$.The area of the circle is $\pi r^2 = \pi \left(\frac{3}{4}\right)^2 = \frac{9\pi}{16}$ square units.

The area of a circle having the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as two of its tangents is:

Similar Questions

Two circles in the first quadrant of radii $r_1$ and $r_2$ touch the coordinate axes. Each of them cuts off an intercept of $2$ units with the line $x+y=2$. Then $r_1^2+r_2^2-r_1 r_2$ is equal to $...........$

The sum of the minimum and maximum distances of the point $(4,-3)$ to the circle $x^2+y^2+4x-10y-7=0$ is

If $C(\alpha, \beta)$ with $\alpha < 0$ is the centre of the circle that touches the $Y$-axis at $(0, 3)$ and makes an intercept of length $2$ units on the positive $X$-axis,then $(\alpha, \beta) =$

The tangents are drawn from the point $(4, 5)$ to the circle $x^2 + y^2 - 4x - 2y - 11 = 0$. The area of the quadrilateral formed by these tangents and the radii is .............. $sq. \text{ units}$.

The angle between the circles $x^2+y^2-4x-6y-3=0$ and $x^2+y^2+8x-4y+11=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module